How do you write the partial fraction decomposition of the rational expression # x/((x+7)(x+8)(x+9))#?
1 Answer
Aug 7, 2016
Explanation:
#x/((x+7)(x+8)(x+9)) = A/(x+7)+B/(x+8)+C/(x+9)#
Using Heaviside's cover-up method, we find:
#A = (-7)/(((-7)+8)((-7)+9)) = (-7)/2 = -7/2#
#B = (-8)/(((-8)+7)((-8)+9)) = (-8)/(-1) = 8#
#C = (-9)/(((-9)+7)((-9)+8)) = (-9)/2 = -9/2#
So:
#x/((x+7)(x+8)(x+9)) = -7/(2(x+7))+8/(x+8)-9/(2(x+9))#
